Pith Number

pith:6AT6QMSJ

pith:2018:6AT6QMSJJVNRFE7AMHEK5LCRJB

not attested not anchored not stored refs pending

Combinatorial modifications of Reeb graphs and the realization problem

{\L}ukasz Patryk Michalak

arxiv:1811.08031 v2 · 2018-11-20 · math.GT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6AT6QMSJJVNRFE7AMHEK5LCRJB}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

On Reeb graphs induced from smooth functions on closed or open manifolds

Receipt and verification

First computed	2026-07-05T07:51:21.842692Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f027e832494d5b1293e061c8aeac514841bbf67c963bfe76ea671dd2a29c67f3

Aliases

arxiv: 1811.08031 · arxiv_version: 1811.08031v2 · doi: 10.48550/arxiv.1811.08031 · pith_short_12: 6AT6QMSJJVNR · pith_short_16: 6AT6QMSJJVNRFE7A · pith_short_8: 6AT6QMSJ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6AT6QMSJJVNRFE7AMHEK5LCRJB \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: f027e832494d5b1293e061c8aeac514841bbf67c963bfe76ea671dd2a29c67f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aaf1c430f0d132e49e74959b6a503488dd0622bc429880306de44b71ac719d00",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2018-11-20T00:26:12Z",
    "title_canon_sha256": "9a8c9b11f48fa917bce474ddcfefe14f6a051b9ae081690846231c32f4be1bec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.08031",
    "kind": "arxiv",
    "version": 2
  }
}